ALREADY acting the part of a slick politician, Hollywood uberhunk Arnold Schwarzenegger used a brief photo-op yesterday to butter up key Republican ally Mayor Giuliani.

Schwarzenegger, who recently admitted he’s “exploring running for governor” of California in 2002, won over Giuliani by spouting a laundry list of positive statistics about New York City during a lavish Times Square promotion for a new General Motors off-road truck.

But moments after the two chummy Republicans posed for cameras, Giuliani ducked out with his aides and Schwarzenegger answered questions – but only about GM.

When “The Terminator” was pressed about the 2002 gubernatorial race in his home state, Schwarzenegger’s pit-bull publicist, Jill Eisenstadt, shoved microphones away.

SCHWARZENEGGER may be wise to remain coy. Although California Gov. Gray Davis, a Democrat, is bumbling his way through the state’s energy crisis, the timing may not be perfect for Ah-nald the Action Hero to steal the scene.

First, he has a few skeletons to stuff in the closet.

Last month, Schwarzenegger, who has four children with Kennedy-clan member Maria Shriver, was the subject of a scathing Premiere magazine article alleging vile sexual high jinks on the sets of his movies.

The anonymously sourced accusations are wide-ranging.

On the set of “Terminator 2: Judgment Day,” in 1991, Schwarzenegger reportedly reached inside a crew member’s blouse and pulled her breasts out of her bra. Another source claims Schwarzenegger fondled co-star Linda Hamilton during a limousine ride with the film’s director, James Cameron, present.

The article reported Schwarzenegger was caught having sex with an unidentified woman in his trailer on the set of 1996’s “Eraser.” He’s also accused of having an affair with his “Total Recall” co-star, Rachel Ticotin.

One witness claimed Shriver was aware of her husband’s roving.

“This guy is a real pig,” one Hollywood lawyer told Premiere reporter John Connolly. “He will say the most disgusting sexual things to women he doesn’t know.”

Premiere was bombarded with blistering denials from Schwarzenegger’s former co-stars, directors and producers.

Hamilton and Cameron wrote vehement letters refuting the stories involving them. Cameron, who has made four films with Schwarzenegger, stated he has “never seen Arnold act in the course fashion you describe with any woman, at any time, ever.”

Co-stars Kelly Preston, Rita Wilson and Jamie Lee Curtis all chimed in, painting Schwarzenegger as a devoted family man with a thoroughly professional work ethic.

Curtis, a self-described liberal Democrat, called the article a “politically motivated hatchet job,” and she might not be far off.

In a preemptive strike at Schwarzenegger, Davis’ chief strategist, Garry South, faxed the Premiere article to 200 political reporters with snide quips at Schwarzenegger’s expense on the cover sheets.

When Schwarzenegger’s lawyer objected, South issued a combative statement.

“We’ll be ready if he comes at us,” South said. “We don’t roll over and play dead for anybody, regardless of the size of his bankroll or biceps.”

But the bravado in Davis’ camp may hide a deep fear of Schwarzenegger’s viability. With the energy crisis escalating, California Democrats could be having nightmares about Schwarzenegger’s growing fan base – which champions the slogan, “Hasta la vista, Davis.”

YET Schwarzenegger is hardly in the clear. The questions about his character reach back decades.

Throughout his weightlifting career, during which he became the only person in history to sweep the Mr. Universe, Mr. World and Mr. Olympia titles in one year (1970), Schwarzenegger used steroids.

While he’s occasionally eluded questions about the topic, in a 1976 interview with The Post, Arnold freely admitted, “I take steroids a few weeks before a competition.”

Besides having to face questions about steroid use, Schwarzenegger is certain to be grilled on his friendship and support for former-Nazi Kurt Waldheim.

In 1986, Waldheim sent life-size, papier-maché statues of Arnold and Maria to the couple as a wedding gift – one that may come to haunt Schwarzenegger’s political aspirations.

In an unauthorized 1990 biography by Wendy Leigh, some former acquaintances of Schwarzenegger alleged he made anti-Semitic, pro-Nazi and racist comments in his early adulthood.

The book also claimed Schwarzenegger’s father, Gustav, a police chief, was accepted into the Nazi Party in 1938. Leigh’s book had also accused Schwarzenegger of womanizing.

Schwarzenegger waged a relentless campaign to discredit Leigh’s book. He won a 1989 libel suit against the British tabloid the News of the World in which he was described as “a secret fan of Adolf Hitler” and someone who “held Nazi and anti-Semitic views,” in a article citing Leigh’s manuscript as a source.

Schwarzenegger is offering a kinder, gentler version of himself. He says he has “sensible” views on gun control, is “socially liberal and fiscally conservative.” He even supports abortion rights.

And his name is being enthusiastically bandied about in Washington.

With Republicans trying to ride out the short wave from Bush’s narrow presidential victory, Beltway pols think Schwarzenegger’s recognizable face – as well as his bottomless accounts – could inject the national party with some much-needed spice if he ran for office.

“I think it’s a wonderful idea,” Sen. Fred Thompson (R-Tenn.) told The Post as he stood just off the Senate floor. “People are looking for politicians outside the system. And celebrity can be good.”

Even Barbara Boxer, the liberal Democratic senator from California, couldn’t think of any reason why Schwarzenegger shouldn’t seek a nomination.

“Everybody has a right to run,” she said. “I don’t look at actors in any special way. They have their own opinion and own ideas about doing things.”

Thompson, who has dabbled on the big screen, hedges his praise.

“The only thing I need to add is that it’s kind of presumptuous for these guys to think they can jump into politics without knowing a thing.”